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As a woman walks, her entire weight is momentarily placed on one heel of her high-heeled shoes. Calculate the pressure exerted on the floor by the heel if it has an area of $1.50 \textrm{ cm}^2$ and the woman's mass is 55.0 kg. Express the pressure in Pa. (In the early days of commercial flight, women were not allowed to wear high-heeled shoes because aircraft floors were too thin to withstand such large pressures.)
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Final Answer

$3.59 \times 10^6 \textrm{ Pa}$

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OpenStax College Physics Solution, Chapter 11, Problem 11 (Problems & Exercises) (1:03)

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Video Transcript

This is College Physics Answers with Shaun Dychko. The pressure exerted by the heel of a woman’s high heel shoe is going to equal the force that it exerts divided by its area. So assuming she has only one heel on the floor at a time, that would mean her entire weight which is <i>mg</i> will be on that heel, and this is just before her toe touches the ground, so just the heel. And that’s going to be <i>mg</i> divided by the area of the heel, so that’s 55 kilograms times 9.8 Newtons per kilogram divided by 1.8 squared centimeters of area converted into meters in order to have our units in Pascal in the end. We need to have Newtons on the top divided by meters squared on the bottom in order to have units in Pascals, because a Pascal is a Newton per meter squared. So we have 1.5 centimeters squared times one over 100 centimeters squared, and this works out to 3.59 times ten to the six Pascal.